Why aren't wireless handshakes sent using TLS? It seems like it would be relatively simple to implement, perhaps having the vendor insert the private key into the routers. That way WPA/WPA2/WEP encryption couldn't be cracked by capturing parts of the handshake sent in plain text.
SSL relies in TCP/IP. TCP/IP relies on the physical and data link layer to have been established. WiFi is part of physical and data link layers. The idea being that you need the lower level links to be established before you can carry on a conversation at the high level.
It's a little like asking why can't a distant person who's only reachable by radio communicate the frequency to listen on in english. Because to communicate in english, you first have to have a radio link, which means knowing the frequency.
Well, first of all TLS is on a totally DIFFERENT OSI level than 802.11 802.11 is on layer 2, TLS is on layer 3/4/5 (it has a few parts) so you simple can not use it in this manner. and modifying it for that purpose is just as hard as creating (what they have done) a new one.
The handshake is not send in 'plaintext', its semi-ciphered. (similarly as how a RSA handshake works). the only reason it's "crackable" is because you always end up with a system that can be cracked. (you have to yield to much information to the environment) the only method to prevent it is by using more aggressive cipher switching (costs a lot more computational power, and limits bandwidth).
EAP-TLS works on a later state than when the handshake between router / client happens) (layer 3/4)
just adding 'crytoware' to a line does NOT mean its more secure. and having it work for all devices is a problem that is still not fully solved.